ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS

ISOMORPHISM OF MODULAR GROUP ALGEBRAS OF ABELIAN GROUPS WITH SEMI-COMPLETE p-PRIMARY COMPONENTS

Let G be a p-mixed abelian group with semi-complete torsion subgroup $G_t$ such that G is splitting or is of torsion-free rank one, and let R be a commutative unitary ring of prime characteristic p. It is proved that the group algebras RG and RH are R-isomorphic for any group H if and only if G and H are isomorphic. This isomorphism relationship extends our earlier results in (Southeast Asian Bull. Math., 2002), (Proc. Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) as well as completely settles a problem posed by W. May in (Proc. Amer. Math. Soc., 1979).